Spectral estimates of a wind fluctuation statistic pertaining to wind energy generators

An estimate is developed for the frequency with which a volume average of the longitudinal component of wind velocity changes by a given amount in a given time. First, a general stochastic model for the longitudinal component of atmospheric turbulence is explicitly constructed. Second, the mathematical foundations on which this paper rests are stated. They include Rice's theorem on level crossings and a modification of the power spectrum for the longitudinal wind component to account for the volume averaging induced by a windmill rotor. Third, these mathematical results are applied to the general wind model to obtain an estimate of the frequency described above in terms of general spectral information. Fourth, attention is restricted to a stochastic wind model based on the theory of isotropic turbulence in order to obtain this estimate in terms of commonly available spectral information. A summary and sample calculations are provided.